diff --git a/2672.patch b/2672.patch
new file mode 100644
index 0000000..5d9ffcb
--- /dev/null
+++ b/2672.patch
@@ -0,0 +1,90 @@
+From 478898b37a91836a39d046f8c70e26c6c9fc06c7 Mon Sep 17 00:00:00 2001
+From: Marius Hillenbrand <mhillen@linux.ibm.com>
+Date: Wed, 17 Jun 2020 16:08:48 +0200
+Subject: [PATCH 1/2] cpp_thread_test/dgemv: cap concurrency to number of hw
+ threads on small systems
+
+... instead of (number of hw threads - 4) to avoid invalid numbers on
+smaller systems. Currently, systems with 4 or fewer CPUs (e.g., small CI
+VMs) would fail the test. Fixes one of the issues discussed in #2668
+
+Signed-off-by: Marius Hillenbrand <mhillen@linux.ibm.com>
+---
+ cpp_thread_test/dgemv_thread_safety.cpp | 2 +-
+ 1 file changed, 1 insertion(+), 1 deletion(-)
+
+diff --git a/cpp_thread_test/dgemv_thread_safety.cpp b/cpp_thread_test/dgemv_thread_safety.cpp
+index 5411fec29..277594ff0 100644
+--- a/cpp_thread_test/dgemv_thread_safety.cpp
++++ b/cpp_thread_test/dgemv_thread_safety.cpp
+@@ -18,7 +18,7 @@ int main(int argc, char* argv[]){
+ 	uint32_t maxHwThreads = omp_get_max_threads();
+ 	
+ 	if (maxHwThreads < 52)
+-		numConcurrentThreads = maxHwThreads -4;
++		numConcurrentThreads = maxHwThreads;
+ 	
+ 	if (argc > 4){
+ 		std::cout<<"ERROR: too many arguments for thread safety tester"<<std::endl;
+
+From de838c38ef9db98a635de1dcedeba8b578ec87b3 Mon Sep 17 00:00:00 2001
+From: Marius Hillenbrand <mhillen@linux.ibm.com>
+Date: Wed, 17 Jun 2020 16:15:44 +0200
+Subject: [PATCH 2/2] cpp_thread_test/dgemv: fail early if concurrency is zero
+
+The two test cases dgemv_tester and dgemm_tester accept the degree of
+concurrency as command line argument (amongst others). Fail early if
+value 0 has been specified, instead of later with less-clear symptoms.
+
+Signed-off-by: Marius Hillenbrand <mhillen@linux.ibm.com>
+---
+ cpp_thread_test/cpp_thread_safety_common.h | 8 ++++++++
+ cpp_thread_test/dgemm_thread_safety.cpp    | 2 ++
+ cpp_thread_test/dgemv_thread_safety.cpp    | 2 ++
+ 3 files changed, 12 insertions(+)
+
+diff --git a/cpp_thread_test/cpp_thread_safety_common.h b/cpp_thread_test/cpp_thread_safety_common.h
+index 60ab5bb2f..8005369a8 100644
+--- a/cpp_thread_test/cpp_thread_safety_common.h
++++ b/cpp_thread_test/cpp_thread_safety_common.h
+@@ -5,6 +5,14 @@ inline void pauser(){
+     std::getline(std::cin, dummy);
+ }
+ 
++void FailIfThreadsAreZero(uint32_t numConcurrentThreads) {
++	if(numConcurrentThreads == 0) {
++		std::cout<<"ERROR: Invalid parameter 0 for number of concurrent calls into OpenBLAS!"<<std::endl;
++		std::cout<<"CBLAS DGEMV thread safety test FAILED!"<<std::endl;
++		exit(-1);
++	}
++}
++
+ void FillMatrices(std::vector<std::vector<double>>& matBlock, std::mt19937_64& PRNG, std::uniform_real_distribution<double>& rngdist, const blasint randomMatSize, const uint32_t numConcurrentThreads, const uint32_t numMat){
+ 	for(uint32_t i=0; i<numMat; i++){
+ 		for(uint32_t j = 0; j < static_cast<uint32_t>(randomMatSize*randomMatSize); j++){
+diff --git a/cpp_thread_test/dgemm_thread_safety.cpp b/cpp_thread_test/dgemm_thread_safety.cpp
+index 1c5287524..104c64f2a 100644
+--- a/cpp_thread_test/dgemm_thread_safety.cpp
++++ b/cpp_thread_test/dgemm_thread_safety.cpp
+@@ -46,6 +46,8 @@ int main(int argc, char* argv[]){
+ 	std::cout<<"Number of concurrent calls into OpenBLAS : "<<numConcurrentThreads<<'\n';
+ 	std::cout<<"Number of testing rounds : "<<numTestRounds<<'\n';
+ 	std::cout<<"This test will need "<<(static_cast<uint64_t>(randomMatSize*randomMatSize)*numConcurrentThreads*3*8)/static_cast<double>(1024*1024)<<" MiB of RAM\n"<<std::endl;
++
++	FailIfThreadsAreZero(numConcurrentThreads);
+ 	
+ 	std::cout<<"Initializing random number generator..."<<std::flush;
+ 	std::mt19937_64 PRNG = InitPRNG();
+diff --git a/cpp_thread_test/dgemv_thread_safety.cpp b/cpp_thread_test/dgemv_thread_safety.cpp
+index 277594ff0..20ea38138 100644
+--- a/cpp_thread_test/dgemv_thread_safety.cpp
++++ b/cpp_thread_test/dgemv_thread_safety.cpp
+@@ -47,6 +47,8 @@ int main(int argc, char* argv[]){
+ 	std::cout<<"Number of concurrent calls into OpenBLAS : "<<numConcurrentThreads<<'\n';
+ 	std::cout<<"Number of testing rounds : "<<numTestRounds<<'\n';
+ 	std::cout<<"This test will need "<<((static_cast<uint64_t>(randomMatSize*randomMatSize)*numConcurrentThreads*8)+(static_cast<uint64_t>(randomMatSize)*numConcurrentThreads*8*2))/static_cast<double>(1024*1024)<<" MiB of RAM\n"<<std::endl;
++
++	FailIfThreadsAreZero(numConcurrentThreads);
+ 	
+ 	std::cout<<"Initializing random number generator..."<<std::flush;
+ 	std::mt19937_64 PRNG = InitPRNG();
diff --git a/openblas.spec b/openblas.spec
index fc36f69..6938e41 100644
--- a/openblas.spec
+++ b/openblas.spec
@@ -15,7 +15,7 @@
 
 Name:           openblas
 Version:        0.3.10
-Release:        1%{?dist}
+Release:        2%{?dist}
 Summary:        An optimized BLAS library based on GotoBLAS2
 License:        BSD
 URL:            https://github.com/xianyi/OpenBLAS/
@@ -30,7 +30,10 @@ Patch2:         openblas-0.2.15-constructor.patch
 Patch3:         openblas-0.3.7-tests.patch
 
 # Fix broken detection for z13 support
-Patch4:         https://patch-diff.githubusercontent.com/raw/xianyi/OpenBLAS/pull/2669.patch
+Patch4:         https://github.com/xianyi/OpenBLAS/pull/2669.patch
+
+# Fix test suite failure for <= 4 CPUs
+Patch5:         https://github.com/xianyi/OpenBLAS/pull/2672.patch
 
 BuildRequires:  gcc
 BuildRequires:  gcc-c++
@@ -245,6 +248,7 @@ cd OpenBLAS-%{version}
 %endif
 %patch3 -p1 -b .tests
 %patch4 -p1 -b .s390x
+%patch5 -p1 -b .fewcpus
 
 # Fix source permissions
 find -name \*.f -exec chmod 644 {} \;
@@ -668,6 +672,9 @@ rm -rf %{buildroot}%{_libdir}/pkgconfig
 %endif
 
 %changelog
+* Tue Jul 28 2020 Susi Lehtola <jussilehtola@fedoraproject.org> - 0.3.10-2
+- Include upstream patch 2672 to fix test suite on systems with few CPUs.
+
 * Mon Jun 15 2020 Susi Lehtola <jussilehtola@fedoraproject.org> - 0.3.10-1
 - Update to 0.3.10.